Stabilized transistor amplifier

ABSTRACT

A stabilized transistor amplifier including an amplifying transistor and its biasing circuit consisting of such elements as a power supply source, diodes and resistors in which several circuit constrants of the biasing circuit at a certain pre-selected temperature are selected so as to compensate for or cancel changes in characteristic of the amplifying transistor, the power supply source, the diodes and the resistors in combination, so that the amplifier operates stably over a wide range of the ambient temperature.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to a transistor amplifier and moreparticularly to a stabilized transistor amplifier.

2. Description of the Prior Art

A lot of efforts have been made in the technical field to provide astabilized transistor amplifier regardless of ambient temperaturevariations and several practical circuit arrangements for such a purposeare well known in the prior art.

However, in most of such known circuit arrangements, attention has beenpaid only to changes in characteristic of semiconductors used in thecircuit and not to changes in characteristic of a power supply voltageand resistors used in the same circuit when the ambient temperaturechanges, so that the circuits often do not operate satisfactorily over awide range of the ambient temperature under the influence of the changesin characteristic of the power supply voltage and the resistors.

OBJECTS OF THE INVENTION

Accordingly, it is an object of this invention to provide an improvedand novel stabilized transistor amplifier avoiding disadvantagesinherent to the prior art.

It is another object of this invention to provide an improved stabilizedamplifier which operates with superior stability over a wide range ofthe ambient temperature.

It is a further object of this invention to provide an improvedtransistor amplifier stabilized over a wide range of the ambienttemperature regardless not only of changes in characteristic ofsemiconductive devices, but also of changes in characteristic of a powersupply voltage and resistors used in the same circuit.

SUMMARY OF THE INVENTION

In a transistor amplifier according to this invention, attention is paidnot only to changes in characteristic of semiconductor devices used inthe circuit, but also to changes in characteristic of a power supplyvoltage and resistors used in the same circuit, and all of such changesas mentioned above are compensated for or cancelled by selecting theinitial condition of several circuit constants at a certain pre-selectedambient temperature.

The features of the invention are set forth with particularity in theappended claims. The invention itself, however, both as to itsorganization and method of operation, together with further objects andadvantages thereof, may best be understood by reference to the followingdescription taken in connection with the accompanying drawings.

DESCRIPTION OF THE DRAWING

FIG. 1 is a typical stabilized transistor amplifier of the prior art.

FIG. 2 is a simplified diagram for measuring a characteristic of acircuit such as shown in FIG. 1.

FIG. 3 is a graph to be used for explaining the characteristic of thecircuit shown in FIGS. 1 and 2.

FIG. 4 is a principle circuit diagram of the transistor amplifieraccording to the present invention.

FIG. 5 is a circuit diagram showing one example for obtaining the inputvoltage E_(B) in the circuit of FIG. 4.

FIGS. 6 - 11 are embodied circuit diagrams respectively relative to thecircuit of FIG. 4.

FIG. 12 is a circuit diagram showing an embodiment in which the inputvoltage E_(B) is supplied from a constant voltage source and maintainedconstant regardless of the ambient temperature in the circuit of FIG. 4.

FIG. 13 is a circuit diagram showing an embodiment in which the inputvoltage E_(B) is obtained by adopting a constant current source in thecircuit of FIG. 4.

FIG. 14 is a circuit diagram showing one example of the constant currentsource of the circuit shown in FIG. 13.

FIGS. 15 and 16 are circuit diagrams showing other examples forobtaining constant current sources in embodied circuits of FIG. 4respectively.

FIG. 17 is another principle circuit diagram of the transistor amplifieraccording to the present invention.

FIG. 18 is a circuit diagram showing one example for obtaining the inputvoltage E_(B) in the circuit of FIG. 17.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

For better understanding this invention, a prior art transistoramplifier circuit will first be described with reference to FIG. 1. Withthe prior art transistor amplifier circuit depicted in FIG. 1, the DCbiasing current for the transistor is constant regardless of the ambienttemperature change.

In the transistor amplifier circuit shown in FIG. 1, between the base ofan amplifying transistor 1 whose emitter is grounded and the groundthere is connected to a diode 2, and between the base of the transistor1 and a voltage source of +E there is connected a resistor 3. With thiscircuit, when the forwardly biased voltage drop across the PN-junctionbetween the base and emitter of the transistor 1 is changed inaccordance with ambient temperature variation, the forwardly biasedvoltage drop across the diode 2 is changed similarly. As a result, a DCbiasing current I_(C) which flows through the collector of thetransistor 1 is constant irrespective of the ambient temperature change.This can be said of the assumption that the resistance value of theresistor 3 is constant irrespective of the ambient temperature change.However, in fact the resistance value of the resistor 3 is changed inaccordance with the ambient temperature change, so that the DC biasingcurrent I_(C) is not constant. If the circuit depicted in FIG. 1 isformed on a single semiconductor wafer as an integrated circuit, thetemperature coefficient of the resistor 3 becomes positive and isrelatively high. As a result, the DC biasing current I_(C) tends todecrease in accordance with increase of the ambient temperature.

FIG. 2 shows a circuit for measuring the DC biasing current I_(C) of theabove circuit formed as an integrated circuit. In the embodiment of FIG.2, a transistor 2 which is substantially same as the transistor 1 inconstruction and whose base and collectors are connected directly isused in place of the diode 2 of the embodiment shown in FIG. 1, and theresistance value of the resistor 3 is selected to be 10 KΩ. When a DCvoltage of 6 volts is applied to the collector of the transistor 1, a DCvoltage of +E is applied to the series circuit of the resistor 3 and thediode 2, and the DC biasing current I_(C) flowing through the collectorof the transistor 1 is measured for the ambient temperature, the resultis shown in FIG. 3 in which the DC voltage E is varied from 6 volts to20 volts 2 volts by successive increments of two volts. In FIG. 2,reference letter A₁ indicates an ammeter inserted into the collectorcircuit of the transistor 1.

As may be seen in FIG. 3, the compensation of the diode 2 for thetransistor 1 becomes to an over-compensation and hence the DC biasingcurrent I_(C) has a negative temperature characteristic.

A stabilized transistor amplifier circuit of this invention, with whicha biasing current is constant positively regardless of the ambienttemperature change, will be described with reference to the drawings.

In this invention, as shown in FIG. 4, the emitter of a transistor 11 isconnected through m diodes D_(a1), -- D_(am) (where m is a positiveinteger) and a resistor R₁ to a reference voltage terminal such as theground terminal, an input voltage E_(B) is applied to the base of thetransistor 11 through a resistor R₂ and k number of diodes D_(b1), --D_(bk) (where b is a positive integer), and the circuit constantsthereof are selected to substantially satisfy the following equation(1).

    αV.sub.10 - βV.sub.20 + γ - (k + m + 1) = 0(1)

where

    α = - K.sub.R /ΔV.sub.BE, β = K.sub.R -K.sub.H /ΔV.sub.BE, γ = ΔE.sub.B /ΔV.sub.BE (2)

and V₁₀ respresents a terminal voltage across the resistor R₁ at acertain pre-selected temperature T₀ ; V₂₀ a terminal voltage across theresistor R₂ at the pre-selected temperature T₀ ; K_(R) the temperaturecoefficient of the resistors R₁ and R₂ ; K_(H) the temperaturecoefficient of the current amplification factor h_(FE) of the transistor11 whose emitter is grounded; ΔE_(B) the increment per degree of theinput voltage E_(B) ; and ΔV_(BE) the increment per degree of theforwardly biased voltage drops the base-emitter of the transistor 11 andthe respective diodes or PN-junction.

In this case, the numbers m and k of the diodes D_(a1), -- D_(am), andD_(b1), -- D_(bk) may be zero and the resistance values of the resistorsR₁ and R₂ may be zero.

In practice, the circuit shown in FIG. 4 is formed on a commonsemiconductor wafer as an integrated circuit.

In the circuit shown in FIG. 4, if the input voltage is E_(BO) and theforwardly biased voltage drop across the base-emitter PN-junction of thetransistor 11 is V₀ at the pre-selected temperature T₀, the followingequation (3) is established from equation (1).

    E.sub.BO - V.sub.10 - V.sub.20 - (k + m + 1) V.sub.0 = 0   (3)

if, further, it is assumed that, at the temperature T_(O), theresistance value of the resistor R₁ is taken as R₁₀ ; that of theresistor R₂ as R₂₀ ; the DC biasing current flowing through the emitterof the transistor 11 as I₁ ; the current flowing into the base of thetransistor 11 as I₂₀ ; and the current amplification factor of thetransistor 11 as h₀, the following equations (4) are established.

    V.sub.10 = R.sub.10 . I.sub.1, V.sub.20 = R.sub.20 . I.sub.20 = R.sub.20 I.sub.1 /h.sub.0                                          (4)

If it is assumed that, at a certain temperature T = T₀ + ΔT, the inputvoltage is taken as E_(B) ; the terminal voltage across the resistor R₁as V₁ ; that across the resistor R₂ as V₂ ; and the forwardly biasedvoltage drop across the PB-junction as V_(BE), the following equation(5) is established.

    E.sub.B - V.sub.1 - V.sub.2 - (k + m + 1)V.sub.BE = 0      (5)

in order to make the DC biasing current I₁ constant even at thearbitrary temperature T = T₀ + ΔT, it is sufficient that the voltages V₁and V₂ in the equation (5) are expressed as follows on the assumptionthat the current amplification factor of the transistor 11 is h_(FE) andthe current flowing into the base of the transistor 11 is I₂.

    v.sub.1 = r.sub.1 . i.sub.1, v.sub.2 = r.sub.2 . i.sub.2 = r.sub.2 i.sub.1 /h.sub.FE                                                 (6)

since the following equation (7) is established defines the change inthe resistance R₁ as a function of temperature,

    R.sub.1 = R.sub.10 (1 + K.sub.R . ΔT)                (7)

the following equation (8) is obtained.

    V.sub.1 = R.sub.10 . I.sub.1 (1 + K.sub.R . ΔT) = V.sub.10 (1 + K.sub.R . ΔT)                                       (8)

further, since the following relationships exist

R₂ = R₂₀ (1 + K_(R) . ΔT) (9)

h_(FE) = h₀ (1 + K_(H) . ΔT) (10)

the voltage V₂ can be expressed as follows. ##EQU1##

In this case, since the following equation (11b) can be approximated##EQU2## the voltage V₂ can be expressed as follows.

    V.sub.2 = V.sub.20 { 1 + (K.sub.R - K.sub.H) ΔT}     (11)

since the following equations (12) and (13) are obtained

E_(B) = E_(BO) + ΔE_(B) . ΔT (12)

v_(be) = v₀ + Δv_(be) . Δt (13)

the following equation (14) is obtained by substituting the equations(8) and (11) to (13) into the equation (5).

    (E.sub.BO + ΔE.sub.B . ΔT) - V.sub.10 (1 + K.sub.R . ΔT) - V.sub.20 {1 + (K.sub.R - K.sub.H) ΔT} - (k + m + 1) (V.sub.0 + ΔV.sub.BE . ΔT) = 0                           (14)

the following equation (15) can be obtained by substituting the equation(3) into the equation (14).

    ΔE.sub.B - K.sub.R . V.sub.10 - (K.sub.R - K.sub.H)V.sub.20 - (k + m + 1)ΔV.sub.BE = 0                                   (15)

if the equation (15) is divided by ΔV_(BE) and arranged, the followingequation (16) is obtained.

    -K.sub.R /ΔV.sub.BE V.sub.10 -K.sub.R - K.sub.H /ΔV.sub.BE V.sub.20 +ΔE.sub.B /ΔV.sub.BE - (k + m + 1) = 0(16)

If the equation (2) is substituted into the equation (16), the equation(1) is derived.

Therefore, the circuit constants are selected to substantially satisfythe equation (1), the DC biasing current I₁ can be always held constantregardless of the ambient temperature change. This will mean that thecollector biasing current I_(C) of the transistor 11 is held constant.

A practical embodiment which may produce the input voltage E_(B) will bedescribed with reference to FIG. 5. As shown in FIG. 5, it is consideredas the input voltage E_(B) that a source voltage +E is divided by aseries connection of a resistor R₄ and n diodes D_(c1), -- D_(cn), and aseries connection of a resistor R₃ and diodes D_(d1), -- D_(dl). In thiscase, the numbers n and l of the diodes could be zero and the resistancevalues of the resistors R₃ and R₄ could be zero.

In the case where the input voltage E_(B) is obtained by the abovecircuit construction, it is assumed that, at the pre-selectedtemperature T₀, the terminal voltage across the resistor R₃ is taken asV₃₀ ; that across the resistor R₄ as V₄₀ ; and the increment per degreeof the source voltage +E as ΔE. Thus, the following equation (17) isobtained.

    ΔE/ΔV.sub.BE = γ'                        (17)

in this case, the following factor (18) is substituted into the equation(1) instead of γ. ##EQU3##

Thus, the following equation (19) is derived. ##EQU4##

If the circuit constants are selected to approximately satisfy the aboveequation (19), the purpose is achieved.

In this case, at the pre-selected temperature T₀ the following equation(20a) is obtained

    V.sub.30 + lV.sub.0 = V.sub.10 + V.sub.20 + (k + m + 1)V.sub.0(20a)

so that the next equation (20) is established.

    -V.sub.10 - V.sub.20 + V.sub.30 + lV.sub.0 - (k + m + 1)V.sub.0 = 0 (20)

if it is assumed that, at the pre-selected temperature T₀, theresistance value of the resistor R₃ is taken as R₃₀ and the currentflowing through the resistor R₃ as I₃₀, the voltage V₃₀ is expressed asfollows.

    V.sub.30 = R.sub.30 . I.sub.30                             (21)

further, assuming that, at the pre-selected temperature T₀, the sourcevoltage is taken as E₀ ; the resistance value of the resistor R₄ as R₄₀; the current I₂₀ flowing into the base of the transistor 11 isneglected; and the equal current I₃₀ flows through both the resistors R₃and R₄, the current I₃₀ is expressed as follows. ##EQU5##

If the equation (22) is substituted into the equation (21) and then intothe equation (20), the following equation (23) is obtained.

    -V.sub.10 - V.sub.20 + R.sub.30 /R.sub.30 +R.sub.40 (E.sub.0 -nV.sub.0) + R.sub.40 /R.sub.30 +R.sub.40 lV.sub.0 - (k + m + 1) = 0   (23)

If the equal current flows through the resistors R₃ and R₄ as describedabove, the following expressions (24) are established.

    R.sub.30 /R.sub.30 + R.sub.40 = V.sub.30 /V.sub.30 + V.sub.40, R.sub.40 /R.sub.30 + R.sub.40 = V.sub.40 /V.sub.30 + V.sub.40      (24)

if the terminal voltage across the resistor R₃ at the arbitrarytemperature T = T₀ + ΔT is taken as V₃, the following equation (25a) isobtained.

    V.sub.3 + lV.sub.BE = V.sub.1 + V.sub.2 + (k + m + 1)V.sub.BE(25a)

Accordingly, the next equation (25) is established.

    -V.sub.1 - V.sub.2 + V.sub.3 + lV.sub.BE - (k + m + 1)V.sub.BE = 0(25)

if the current flowing through the resistor R₃ at the arbitrarytemperature T = T₀ + ΔT is assumed as I₃, the following expression (26)is obtained.

    V.sub.3 = R.sub.3 . I.sub.3                                (26)

further, if it is assumed at this case that the current I₂ flowing intothe base of the transistor 11 is neglected and the equal current flowsthrough the resistors R₃ and R₄, the current I₃ is expressed asfollows,. ##EQU6##

Thus, if the equation (27) is substituted into the equation (26) andthen into the equation (25), the following equation (28) is obtained.

    -V.sub.1 - V.sub.2 + R.sub.3 /R.sub.3 + R.sub.4 (E - nV.sub.BE) + R.sub.4 /R.sub.3 + R.sub.4 lV.sub.BE - (k + m + 1)V.sub.BE = 0    (28)

in order to make that the DC biasing current I₁ is constant event at thearbitrary temperature T = T₀ + ΔT, it is sufficient that in the equation(28) the voltages V₁ and V₂ are obtained by the equation (6) andaccordingly (8) and (11).

In this case, since the following expressions (29) to (31) are obtained.

R₃ = r₃₀ (1 + k_(r) . Δt) (29)

r₄ = r₄₀ (1 + k_(r) . Δt) (30)

e = e₀ +Δe . Δt (31)

and V_(BE) is given by the equation (13), if the equations (8), (11),(29) to (31) and (13) are substituted into the equation (28), the nextequation (32) is derived.

    -V.sub.10 (1 + K.sub.R . ΔT) - V.sub.20 {1 + (K.sub.R - K.sub.H)ΔT} + R.sub.30 /R.sub.30 + R.sub.40 {(E.sub.0 + ΔE.ΔT) - n)V.sub.0 + ΔV.sub.BE . ΔT)} + R.sub.40 /R.sub.30 + R.sub.40 l(V.sub.0 + ΔV.sub.BE.ΔT) - (k + m + 1)(V.sub.0 + ΔV.sub.BE. ΔT) = 0               (32)

if the equation (23) is substituted into the equation (32), the nextequation (33) is derived.

    -K.sub.R . V.sub.10 - (K.sub.R - K.sub.H) V.sub.20 + R.sub.30 /R.sub.30 + R.sub.40 (ΔE - nΔV.sub.BE) + R.sub.40 /R.sub.30 + R.sub.40 lΔV.sub.BE - (k + m + 11 ΔV.sub.BE = 0        (33)

if the equation (33) is divided by ΔV_(BE) and the equation (24) issubstituted thereinto, the next equation (34) is derived. ##EQU7##

Accordingly, if α, β and γ' are used in the equation (34) as in the caseof the equations (2) and (17), it can be expressed similar to theequation (19).

As may be apparent from the foregoing, in the case that the inputvoltage E_(B) is produced by the circuit shown in FIG. 5, if the circuitconstants are selected to satisfy the equation (19) substantially, theDC biasing current I₁ can be made constant always irrespective of theambient temperature change.

Based upon the circuit shown in FIG. 5, are various practical circuits.FIG. 6 shows one of such examples in which the biasing circuit for thetransistor 11 is formed of the resistors R₁ to R₄ only; FIG. 7 showsanother example in which only one diode D_(d1) is connected in series tothe resistor R₃ of the biasing circuit shown in FIG. 6, FIG. 8 shows afurther embodiment in which only one diode D_(c1) is connected in seriesto the resistor R₄ of the biasing circuit shown in FIG. 6; FIG. 9 showsa yet further example in which only one diode D_(a1) is connected inseries to the resistor R₁ of the biasing circuit shown in FIG. 6; andFIG. 10 shows a still further example in which one diode D_(b1) isconnected to the base of the transistor 11. It is also possible that aplurality of diodes D_(a1), D_(a2), D_(c1) and D_(d1) are connected asshown in FIG. 11. In any case, it is necessary that the circuitconstants of the above circuits must be selected to satisfy the equation(19).

In the above explanation, it is to be noted that the equation (19) is aspecial case of the equation (1) and hence the former equation isincluded in the latter one. That is, several other equations may bederived from the equation (1) when certain special conditions are given.

If such a condition that the input voltage E_(B) in FIG. 4 is heldconstant regardless of the ambient temperature change is given, thecircuit constants thereof are selected to approximately satisfy thefollowing equation (35) for making the circuit shown in FIG. 4 stablerelative to the ambient temperature.

    αV.sub.10 - βV.sub.20 - (k + m + 1) = 0         (35)

In detail, in the case that the input voltage E_(B) is given by aconstant voltage circuit 12 at the pre-stage as shown in FIG. 12, sinceΔE_(B) = 0 is held in the equation (2), γ = 0. Therefore, if the circuitconstants are selected to substantially satisfy the equation (35) whichis same as the case where γ = 0 in the equation (1), the DC biasingcurrents I₁ and I_(C) become always constant regardless of the ambienttemperature change. While, in the case that the input voltage E_(B) isobtained by the circuit shown in FIG. 5, even if the source voltage Edepends upon the ambient temperature, the equation (18) corresponding toγ in the equation (1) is zero. Accordingly, if the following equation(36) is satisfied

    (γ' - n) V.sub.30 + lV.sub.40 = 0                    (36)

the input voltage E_(B) becomes constant irrespective of the ambienttemperature change. Thus, if the equation (35) is satisfied under thecondition, the DC biasing currents I₁ and I_(C) are made constantregardless of the ambient temperature change.

Assuming that such a condition that the input voltage E_(B) is givenfrom the source voltage +E through the series connection of the resistorR₄ and the n's number of diodes D_(c1) to D_(cn) and the current flowingthrough the resistor R₄ is constant regardless of the ambienttemperature change is given. If the terminal voltage across the resistorR₄ is taken as V₄₀ at the pre-select temperature T₀ ; and in theequation (1) (V₁₀ + V₄₀) is used in place of V₁₀, γ' obtained by theequation (17) is used in place of γ, and (n + k + m + 1) is used inplace of (k + m + 1), the next equation (37) is obtained.

    α(V.sub.10 + V.sub.40) - βV.sub.20 + γ' - (n + k + m + 1) = 0                                                       (37)

Accordingly, if the circuit constants are selected to satisfy theequation (37), the given condition is obtained.

In this case, at the temperature T₀ the next equation (38a) isestablished.

    E.sub.0 = V.sub.10 + V.sub.20 + V.sub.40 + (n + k + m + 1) V.sub.0 (38a)

Thus, the next equation (38) is obtained.

    -(V.sub.10 + V.sub.40) - V.sub.20 + E.sub.0 - (n + k + m + 1) V.sub.0 = 0 (38)

while, at the arbitrary temperature T = T₀ + ΔT the following equation(39a) is established.

    E = V.sub.1 + V.sub.2 + V.sub.4 + (n + k + m + 1) V.sub.BE = 0 (39a)

Thus, the next equation (39) is obtained.

    -(V.sub.1 + V.sub.4) - V.sub.2 + E - (n + k + m + 1) V.sub.BE = 0  (39)

in this case, since the current I₄ flowing through the resistor R₄ isalways constant, the voltage V₄ is expressed as follows.

V₄ = R₄ . I₄

= r₄₀ . i₄ (1 + k_(r) . Δt)

= v₄₀ (1 + k_(r) . Δt) (40)

in order to make the DC biasing current I₁ constant at the arbitrarytemperature T = T₀ + ΔT, it is sufficient that in the equation (39) V₁and V₂ are obtained by the equation (6) and accordingly (8) and (11).Thus, if the equations (8), (11), (13), (31) and (40) are substitutedinto the equation (39), the next equation (41) is obtained.

    -(V.sub.10 + V.sub.40) (1 + K.sub.R . ΔT) - V.sub.20 {1 + (K.sub.R - K.sub.H) ΔT}+(E.sub.0 + ΔE . ΔT) - (n + k + m + 1) (V.sub.0 + ΔV.sub.BE . ΔT) = 0                (41)

then, if the equation (38) is substituted into the equation (41), thenext equation (42) is obtained.

    -K.sub.R (V.sub.10 + V.sub.40) - (K.sub.R - K.sub.H) V.sub.20 + ΔE - (n + k + m +0 1) ΔV.sub.BE = 0                      (42)

thus, the following equation (43) is obtained by dividing the equation(42) with ΔV_(BE).

    - k.sub.r /Δv.sub.be (v.sub.10 + v.sub.40) - k.sub.r - k.sub.h /Δv.sub.be v.sub.20 + Δe/Δv.sub.be - (n + k + m + 1) = 0(43)

Accordingly, α, β and γ' are used in the equation (43) as in the case ofthe equations (2) and (17), the equation similar to that (37) isobtained.

With the circuit shown in FIG. 13, if the current I₄ flowing through theresistor R₄ is constant, by selecting the circuit constants to satisfythe equation (37) substantially, the DC biasing current I₁ can be madeconstant.

In order to make the current I₄ flowing through the resistor R₄ in thecircuit of FIG. 13 constant, there are two methods. The first method isthat, as shown in FIG. 14, a transistor 13 is connected at the pre-stageof the circuit, the input voltage E_(B) is derived as the collectorvoltage of the transistor 13, and a current control circuit 14 isconnected to the base of the transistor 13 to make the collector currentof the transistor 13 constant. The second method is that, as shown inFIG. 5, in the case of connecting the resistor R₃ and l's diodesD_(d1) - D_(d) in the ground side of the circuit, if the current I₂flowing into the base of the transistor 11 is neglected and hence thecurrents I₃ and I₄ flowing through the resistors R₃ and R₄ are taken asequal, it is necessary to make the currents constant regardless of thetemperature.

The second method will be described in detail. If I₃ = I₄ = I, thecurrent I can be expressed similar to the equation (27) as follows.##EQU8##

If the equations (29) to (31) and (13) are substituted into the equation(44), the current I is expressed as follows. ##EQU9##

Accordingly, if the following term (46a) is 0 ##EQU10## or the followingequation (46) is satisfied,

    -K.sub.R (V.sub.30 + V.sub.40) + ΔE - (n + l) ΔV.sub.BE = 0(46)

the current I becomes constant.

If the equation (46) is divided by ΔV_(EB), the next equation (47a) andaccordingly (47) are obtained.

- K_(R) /ΔV_(BE) (V₃₀ + V₄₀) + ΔE/ΔV_(BE) - (n + l) = 0 (47a)

α(V₃₀ + V₄₀) + γ' - (n + l) = 0 (47)

Accordingly, in the latter case if the circuit constants are selected tosatisfy both the equations (47) and (37), the DC biasing current I₁becomes constant.

In this case, when (k + m + 1) = l and R₂ = 0 or V₂₀ = 0 as in the caseof FIG. 15 or FIG. 16, V₁₀ = V₃₀ is satisfied. Therefore, the equation(47) coincides with the equation (37), so that in this case it issufficient to select the circuit constants so as to satisfy the equation(37) or (47).

In the circuits shown in FIGS. 4 - 5 and 7 - 16, one or plurality ofdiodes are used, and in practice the diodes are formed of transistorswhose bases and collectors are connected directly, but it may possibleto employ transistors whose bases and collectors are connected throughresistors in place of the diodes, as described later.

FIG. 17 shows a circuit in which a transistor whose base and collectorare connected through a resistor is used in place of the diode used inthe circuit of FIG. 4.

In the circuit of FIG. 17, the emitter of the transistor 11 is connectedto the reference voltage terminal such as the ground terminal throughm's number of transistors T_(m1) to T_(mm) whose bases and collectorsare connected through resistors R_(m1) to R_(mm), respectively, andthrough the resistor R₁. The base of the transistor 11 is supplied withthe input voltage E_(B) through the resistor R₂ and through k's numberof transistors T_(k1) to T_(kk) whose bases and collectors are connectedthrough resistors R_(k1) to R_(kk), respectively.

If the circuit constants of the circuit shown in FIG. 17 are selected tosubstantially satisfy the next equation (48),

    αV.sub.10 - β(V.sub.20 + V.sub.m0) - δV.sub.k0 + γ - (k + m + 1) = 0                                           (48)

the circuit of FIG. 17 becomes stable for the ambient temperature, asdescribed below in detail.

In the equation (48), δ is expressed as follows,

    δ = K.sub.R - 2K.sub.H /ΔV.sub.BE              (49)

v_(m0) is the total voltage of the terminal voltages across therespective resistors R_(m1) to R_(mm) connected to the transistorsT_(m1) to T_(mm) which are, in turn, connected to the emitter of thetransistor 11 at the pre-selected temperature T₀, and V_(k0) the totalvoltage of the terminal voltages across the respective resistors R_(k1)to R_(kk) connected to the transistors T_(k1) to T_(kk) which are, inturn, connected to the base of the transistor 11 at the pre-selectedtemperature T₀.

In this case, it may be possible that the numbers m and k of thetransistors are zero and the resistance values of the resistors R₁ andR₂ are zero.

The equation (48) is derived as follows. In the circuit of FIG. 17, thefollowing equation (50) is established at the pre-selected temperatureT₀.

    e.sub.bo - v.sub.10 - v.sub.20 - v.sub.m0 - V.sub.k0 - (k + m + 1) = 0(50)

If it is assumed that, at the pre-selected temperature T₀, the totalresistance value of the resistance values of the resistors R_(m1) toR_(mm) is taken as R_(m0) ; that of the resistors R_(k1) to R_(kk) takenas R_(k0) ; the current flowing through the resistors R_(m1) to R_(mm)taken as I_(m0) ; and that flowing through the resistors R_(k1) toR_(kk) taken as I_(k0) the current I_(m0) and I_(k0) are expressed asfollows.

    I.sub.m0 = I.sub.1 /h.sub.0, I.sub.kO = I.sub.1 /h.sub.0.sup.2(51)

Therefore, the voltages V_(m0) and V_(k0) are expressed as follows.

    V.sub.m0 = R.sub.m0 . I.sub.m0 = R.sub.m0 . I.sub.1 /h.sub.0 (52)

    V.sub.k0 = R.sub.k0 . I.sub.k0 = R.sub.k0 . I.sub.1 /h.sub.0.spsb.2(53)

If it is assumed at the arbitary temperature T = T₀ + ΔT that the totalterminal voltage across the resistors R_(m1) to R_(mm) is taken as V_(m)and the total terminal voltage across the resistors R_(k1) to R_(kk) asV_(k), the following equation (54) is established.

    E.sub.B - V.sub.1 - V.sub.2 - V.sub.m - V.sub.k - (k + m + 1) V.sub.BE = 0 (54)

in order to make that the DC biasing current I₁ is constant even at thearbitrary temperature T = T₀ + ΔT, the voltages V₁ and V₂ in theequation (54) are given by the equation (6) and accordingly by theequations (8) and (11). Further, if, at the arbitrary temperature T =T₀ + ΔT, the current flowing through the resistors R_(m1) to R_(mm) isassumed as I_(m) and that through the resistors R_(k1) to R_(kk) asI_(k), they are expressed as follows.

    I.sub.m = I.sub.1 /h.sub.FE , I.sub.k = I.sub.1 /h.sub.FE.sup.2 (55)

accordingly, if, at the arbitrary temperature T = T₀ + ΔT, the totalresistance value of the resistors R_(m1) to R_(mm) is assumed as R_(m)and that of the resistors R_(k1) to R_(kk) as R_(k), it is sufficientthat the voltages V_(m) and V_(k) are expressed as follows.

    V.sub.m = R.sub.m. I.sub.m = R.sub.m I.sub.1 /h.sub.FE     (56)

    v.sub.k = R.sub.k . I.sub.k = R.sub.k I.sub.1 /h.sub.FE.sup.2 (57)

since the resistance value R_(m) is expressed as

    R.sub.m = R.sub.m0 (1 + K.sub.R . ΔT)                (58)

and the factor h_(FE) is given by the equation (10), the voltage V_(m)is expressed as follows. ##EQU11##

Further, since the resistance value R_(k) is expressed as

    R.sub.k = R.sub.k0 (1 + K.sub.R.ΔT)                  (60)

the voltage V_(k) is expressed as follows. ##EQU12##

Since the term ##EQU13## is approximately expressed as ##EQU14## thenext equation (61) is obtained.

    V.sub.k = V.sub.k0 {1 + (K.sub.R - 2K.sub.H)ΔT}      (61)

accordingly, if the equations (8), (11) to (13), (59) and (61) aresubstituted into the equation (54), the next equation (62) is obtained.

    (E.sub.BO + ΔE.sub.B . ΔT) - V.sub.10 (1 + K.sub.R . ΔT) - V.sub.20 {  1 + (K.sub.R - K.sub.H)ΔT } - V.sub.mO { 1 + (K.sub.R - K.sub.H)ΔT}- V.sub.kO {1 + (K.sub.R - 2K.sub.H) ΔT} - (k + m + 1) (V.sub.0 + ΔV.sub.EB . ΔT) = 0           (62)

then, if the equation (50) is substituted into the equation (62), thenext equation (63) is obtained.

    ΔE.sub.B - K.sub.R . V.sub.10 - (K.sub.R - K.sub.H) (V.sub.20 + V.sub.m0) - (K.sub.R -2K.sub.H) V.sub.k0 - (k + m + 1) ΔV.sub.BE = 0(63)

if the equation (63) is divided by ΔV_(BE) and then arranged, the nextequation (64) is obtained.

    - K.sub.R /ΔV.sub.BE V.sub.10 - K.sub.R - K.sub.H /ΔV.sub.BE (V.sub.20 + V.sub.m0) - K.sub.R - 2K.sub.H /ΔV.sub.BE V.sub.k0 + ΔE.sub.B /ΔV.sub.BE - (k + m + 1) = 0         (64)

Thus, if the terms α, β, γ and δ are used in the equation (64) as in thecase of the equations (2) and (49), the equation (48) is derived.

In other words, if the circuit constants are selected to substantiallysatisfy the equation (48), the DC biasing current I can be made alwaysconstant regardless of the ambient temperature change.

As a practical embodiment which produces the input voltage E_(B)considered is a circuit as shown in FIG. 18, in which the source voltage+E is divided by a series connection of the resistor R₄, n's number oftransistors T_(n1) to T_(nn) whose bases and collectors are connectedthrough resistors R_(n1) to R_(nn), respectively, and by a seriesconnection of the resistor R₃ and l's number of transistors T₁ to Twhose bases and collectors are connected through resistors R₁ to R. Inthis case, the numbers n and L of the transistors could be zero and theresistance values of the resistors R₃ and R₄ could be zero.

When the input voltage E_(B) is produced by the circuit described above,if it is assumed that the terminal voltages across the resistors R₁, R₂,R₃ and R₄ at the pre-selected temperature T₀ are taken as V₁₀, V₂₀, V₃₀and V₄₀ ; the total voltages of the resistors R_(m1) to R_(mm), R_(k1)to R_(kk), R_(n1) to R_(nn) and R₁ to R at the pre-selected temperatureT₀ are taken as V_(m0), V_(k0), V_(n0) and V₀, respectively; and thefactors α, β, γ' and δ are determined as in the equations (2), (17) and(49), the following equation (65) is obtained. ##EQU15##

Therefore, if the circuit constants are selected to substantiallysatisfy the above equation (65), the purpose is achieved.

As described above, according to the circuit of this invention, the DCbiasing current can be always made constant regardless of the ambienttemperature change and hence the stable amplification operation can beperformed.

It will be apparent that many modifications and variations could beeffected by one skilled in the art without departing from the spiritsand scope of the novel concepts of this invention.

I claim as my invention:
 1. A stabilized amplifier comprising:A. atransistor having base, emitter and collector electrodes; B. circuitmeans comprising m diodes and a first resistor for connecting theemitter electrode of said transistor to a reference voltage terminalwhere m is a positive integer; and C. circuit means comprising k diodesand a second resistor connected in series between the base electrode ofsaid transistor and an input voltage terminal having a voltage value ofE_(B) where k is a positive integer, wherein circuit constants of theamplifier are selected to satisfy the equation:

    αV.sub.10 - βV.sub.20 + γ - (k + m + 1) = 0

where α = - K_(R) /ΔV_(BE), β = k_(r) - k_(h) /Δv_(be), γ = Δe_(b)/Δv_(be), v₁₀ is a voltage drop across the first resistor at a certainpre-selected temperature, V₂₀ is a voltage drop across the secondresistor at the pre-selected temperature, K_(r) is a temperaturecoefficient of the first and second resistors, K_(h) is a temperaturecoefficient of a current amplification factor h_(FE) of the transistorwhen connected as a common emitter configuration, ΔE_(B) is an incrementper degree of the input voltage E_(B), and ΔV_(BE) is an increment perdegree of a voltage drop V_(BE) across a forwardly biased PN junction.2. A stabilized amplifier according to claim 1, wherein said amplifierfurther comprises:
 1. a first series circuit comprising l diodes and athird resistor where l is a positive integer;2. a second series circuitcomprising n diodes and a fourth resistor where n is a positive integer;3. circuit means for connecting said first and second series circuits ina series between a power supply voltage terminal having a voltage valueof E and the reference voltage terminal; and
 4. means for connectingsaid input voltage terminal of E_(B) to a connection point between saidfirst and second series circuits, wherein circuit constants of theamplifier are selected to satisfy the following equation: ##EQU16##where γ' = ΔE/ΔV_(BE),V₃₀ is a voltage drop across the third resistor atthe pre-selected temperature, V₄₀ is a voltage drop across the fourthresistor at the pre-selected temperature, and ΔE is an increment perdegree of the power supply voltage E.
 3. A stabilized amplifieraccording to claim 1, wherein said amplifier further comprises:
 1. aseries circuit comprising n diodes and a resistor R₄ where n is apositive integer;2. a constant current circuit;
 3. circuit means forconnecting said series circuit and said constant current circuit betweena power supply voltage terminal having a voltage value of E and thereference voltage terminal where the constant current circuit makes thecurrent flow through said n diodes and said resistor R₄ substantiallyconstant regardless of the ambient temperature; and
 4. 4. means forconnecting said input voltage terminal of E_(B) to a connection pointbetween said series circuit and said constant current circuit; whereincircuit constants of the amplifier are selected to satisfy the followingequation:

    α(V.sub.10 + V.sub.40) - βV.sub.20 + γ' - (n + k + 1) = 0

where γ' = ΔE/ΔV_(BE) V₄₀ is a voltage drop across the resistor R₄ atthe pre-selected temperature, and ΔE is an increment per degree of thepower supply voltage E.
 4. A stabilized amplifier according to claim 3,wherein said constant current circuit comprises:1. a transistor havingbase, emitter and collector electrodes; kj
 2. current control meansconnected to the base electrode of said transistor; and
 3. circuit meansfor connecting the collector electrode of said transistor to said seriescircuit.
 5. A stabilized amplifier comprising:A. an amplifyingtransistor having base, emitter and collector electrodes; B. circuitmeans comprising m first transistors (T_(m1),--,T_(mm)) and a firstresistor R₁ for connecting the emitter electrode of said amplifyingtransistor to a reference voltage terminal, said m transistors havingbase, emitter and collector electrodes respectively, the base andcollector electrodes thereof being connected by means of resistors(R_(m1),--, R_(mm)) respectively, and the collector-emitter pathsthereof being respectively connected in series with the first resistorR₁ where m is a positive integer; and C. circuit means comprising ksecond transistors (T_(k1),--, T_(kk)) and a second resistor R₂ forconnecting the base electrode of said amplifying transistor to an inputvoltage terminal E_(B), said k of transistors having base, emitter andcollector electrodes respectively, the base and collector electrodesthereof being connected by means of resistors (R_(k1),--, R_(kk))respectively, and the collector - emitter paths thereof beingrespectively connected in series with the second resistor R₂ where k isa positive integer, wherein several circuit constants of the amplifierare selected to satisfy the following equation:

    αV.sub.10 - β(V.sub.20 + V.sub.m0) - δV.sub.k0 + γ - (k + m + 1) = 0

where α = - K_(R) /ΔV_(BE), β = k_(r) - k_(h) /Δv_(be), γ = Δe_(b)/Δv_(be), δ = k_(r) - 2k_(h) /Δv_(be), v₁₀ is a voltage drop across thefirst resistor R₁ at a certain pre-selected temperature, V₂₀ is avoltage drop across the second resistor R₂ at the pre-selectedtemperature, V_(m0) is a total voltage drop across the m of resistors(R_(m1),--, R_(mm)) at the pre-selected temperature, V_(k0) is a totalvoltage drop across the k resistors (R_(k1),--, R_(kk)) at thepre-selected temperature, K_(r) is a temperature coefficient of thefirst and second resistors, the m resistors and the k resistors, K_(h)is a temperature coefficient of a current amplification factor h_(FE) ofthe amplifying transistor, the m transistors and the k transistors wheneach of the transistors is connected as a common-emitter configuration,ΔE_(B) is an increment per degree of the input voltage E_(B), andΔV_(BE) is an increment per degree of a voltage drop V_(BE) across aforwardly biased PN junction.
 6. A stabilized amplifier comprising:A. atransistor having base, emitter, and collector electrodes; B. firstmeans comprising a resistor connecting said emitter to a referencevoltage terminal, said resistor having a temperature co-efficient K_(R); C. an input voltage source having a voltage E_(B) and an increment ofΔE_(B) per degree of temperature at a pre-selected temperature, saidtransistor having a base-emitter voltage drop V_(BE) that changes at anincrement ΔV_(BE) per degree of temperature change at said pre-selectedtemperature; and D. second means connecting said base to said inputvoltage source, where αV₁₀ + γ = 1, α = - k_(r) /Δv_(be), γ = Δe_(b)/Δv_(be), and V₁₀ is the voltage drop across the resistor at saidpre-selected temperature.
 7. The stabilized amplifier of claim 6 inwhich said second means comprises a second resistor having saidtemperature coefficient of K_(R), whereα V₁₀ - βV₂₀ + γ = 1 β = k_(r) -k_(h) /Δv_(be) k_(h) is the temperature coefficient of the currentamplification factor h_(Fe) of the transistor when connected as a commonemitter configuration, and V₂₀ is the voltage drop across said secondresistor at said pre-selected temperature.
 8. The stabilized amplifierof claim 7 comprising, in addition, a series circuit comprising:A. athird resistor connected in series with said second resistor betweensaid voltage source and the base of said transistor; and B. a fourthresistor connected in series with said second resistor between the baseof said transistor and said reference voltage terminal, where

    α V.sub.10 - βV.sub.20 + γV.sub.30 /V.sub.30 + V.sub.40 = 1,

V₃₀ is the voltage drop across the third resistor at said pre-selectedtemperature, and V₄₀ is the voltage drop across the fourth resistor. 9.A stabilized amplifier comprising:A. a transistor having base, emitter,and collector electrodes; B. first means connecting said emitter to areference voltage terminal; C. an input voltage source having a voltageE_(B) and an increment of ΔE_(B) per degree of temperature at apreselected temperature, said transistor having a base-emitter voltagedrop V_(BE) that changes at an increment ΔV_(BE) per degree oftemperature change at said pre-selected temperature; and D. second meanscomprising a resistor connecting said base to said input voltage source,where γ - βV₂₀ = 1, β = k_(r) - k_(h) /Δv_(be), k_(h) is the temperatureco-efficient of the current amplification factor h_(FE) of thetransistor when connected as a common emitter configuration,

    γ = ΔE.sub.B /ΔV.sub.BE, and

V₂₀ is the voltage drop across said resistor at said pre-selectedtemperature.